Asymptotic Stability of Delayed Fractional System with Nonlinear Perturbation

In the present work is considered a nonlinear retarded system of incommensurate type with derivatives in Caputo sense. For this system is cleared the problem with existence and the uniqueness of the solutions of the initial problem in the case of discontinuous initial conditions. As partial case is studied a retarded nonlinear perturbed incommensurate fractional differential system with autonomous linear part. Sufficient conditions are found, which imply that if the zero solution of the linear part of the nonlinear perturbed system is globally asymptotically stable then the zero solution of the perturbed nonlinear system is globally asymptotically stable too.